Quantification of the characteristics of antagonists exhibiting both competitive antagonism and functional interaction.

Null equations have been derived which, when applied to log10 concentration-tissue state curves for an agonist determined in the presence and absence of a competitive antagonist which also exhibits functional interaction, allow quantitation of the characteristics of the competitive and functional interactant effects. Both the affinity constant of the antagonist for its receptors and numerical values characterizing the functional interaction can be obtained. The null equations have been tested in a model system by using a mixture of papaverine hydrochloride (either 5 or 20 microM) and methyl atropine bromide (10 nM) to mimic a competitive antagonist which also shows functional interaction. Agreement between values derived directly and indirectly from the model is good and validates the use of the null equations.